Discretisations for fluid equations in moving domains have been considered as early as the 1990s, where [1]} considers a finite volume discretisation for Navier-Stokes in a moving domain.
The article [2]} provides an overview of of methods for discretisation of fluid dynamics with evolving domains.
It is interesting to note that the article [3]} considers a method for discretising a non-stationary Stokes in a moving domain using geometrically unfitted meshes and ghost penalties.
